Related papers: Multi-Operator Quantum Uncertainty Relations from …
We introduce inequalities for multi-partite entanglement, derived from the geometry of spin vectors. The criteria are constructed iteratively from cross and dot products between the spins of individual subsystems, each of which may have…
Uncertainty relations play a significant role in drawing a line between classical physics and quantum physics. Since the introduction by Heisenberg, these relations have been considerably explored. However, the effect of quantum…
We introduce a product in all complex normed vector spaces, which generalizes the inner product of complex inner product spaces. Naturally the question occurs whether the Cauchy-Schwarz inequality is fulfilled. We provide a positive answer.…
Bell's inequality for continuous-variable bipartite systems is studied. The inequality is expressed in terms of pseudo-spin operators and quantum expectation values are calculated for generic two-mode squeezed states characterized by a…
Recently, [10,11], the Heisenberg Uncertainty relation and the No-Cloning property in Quantum Mechanics and Quantum Computation, respectively, have been extended to versions of Quantum Mechanics and Quantum Computation which are…
The variance of an observable in a quantum state is usually used to describe Heisenberg uncertainty relation. For mixed states, the variance includes quantum uncertainty and classical uncertainty. By means of the skew information and the…
In this paper we obtain weighted higher order Rellich, weighted Gagliardo-Nirenberg, Trudinger, Caffarelli-Kohn-Nirenberg inequalities and the uncertainty principle for Dunkl operators. Moreover, we introduce an extension of the classical…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…
The uncertainty principle and entanglement are two fundamental, but yet not well understood, features of quantum theory. The uncertainty relation reflects the capability limit in acquiring the knowledge of different physical properties of a…
Notions and results from quantum harmonic analysis, such as the convolution between functions and operators or between two operators, is identified as the appropriate setting for Berezin quantization and Berezin-Lieb inequalities. Based on…
Motivated by some applications to calculating order of poles of certain (local or global) $L$-functions, the author considers a Cauchy-Schwarz type inequality for representations of SU(2).
To find the essential nature of quantum theory has been an important problem for not only theoretical interest but also applications to quantum technologies. In those studies on quantum foundations, the notion of uncertainty plays a primary…
In this work we uncover the mathematical structure of the Schwinger algebra and introduce an almost unitary Schwinger operators which are derived by considering translation operators on a finite lattice. We calculate mathematical relations…
We introduce squeezed vacua in loop quantum gravity, a new overcomplete basis of states that contain prescribable correlations between geometric operators. We study the behavior of long-range correlations and discuss the relevance of these…
In this paper we introduce a new technique for proving norm inequalities in operator ideals with an unitarily invariant norm. Among the well known inequalities which can be proved with this technique are the L\"owner-Heinz inequality,…
An inequality in quantum mechanics, which does not appear to be well known, is derived by elementary means and shown to be quite useful. The inequality applies to 'all' operators and 'all' pairs of quantum states, including mixed states. It…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
We establish in this note some Cauchy-Schwarz-type inequalities on compact K\"{a}hler manifolds, which generalize the classical Khovanskii-Teissier inequalities to higher-dimensional cases. Our proof is to make full use of the mixed…
The paper emphasis the role of unsharpness in the body of Quantum Theory and the relations to the conceptual problems of the Theory. Key words: quantum measurement, unsharpness, effect, positive operator-valued measure